Freezing Point Depression

The Solvent Freezing Point Depression calculator computes the change in the freeze temperature (ΔT_b) of a solvent based on the number of moles of solute (n), the mass of the solvent (M), the ebullioscopic constant (K_f).

INSTRUCTIONS: Choose units and enter the following:

• (n) Number of Moles of Solute
• (K_f)  Cryoscopic Constant in ^oK kg/mol
• (i) van't Hoff factor

Solvent Freeze Point Depression (`DeltaT_b`):  The calculator returns the change in freeze point in degrees centigrade.   However, this can be automatically converted to other temperature units via the pull-down menu.

The Math / Science

The solvent freezing point depression is a colligative property^[3] equation that calculates the new freezing temperature of the solvent after it has been mixed in with a solute. The addition of solutes causes the solvent to become impure, causing the freezing point to depress. However, for the freezing point of the solvent to be depressed, the solute must not contribute to the vapor pressure and must remain in the solvent throughout the phase change. The impurity of the solvent causes a decrease in it's chemical potential^[6], which is the amount of molar Gibbs free energy^[4],[5] one mole of solvent contributes to the mix. A high chemical potential drives the reaction towards product formation, however increasing solute molarity, increases boiling point and decreases chemical potential.

The formula for the change in freezing point of a solvent  is:

               `ΔT<sub>f</sub> = K<sub>f</sub> • m • i`

where:

• `DeltaT_b` is the change in solvent boiling temperature of the solvent in units of (^oC). 
• K_f is the cryoscopic constant, unique for each solvent in units of (^oC kg/mol),. For water, K_f = 1.853 K·kg/mol
• m = molality, number of moles of solute per kg of solvent (mol/kg)
• i = van't Hoff factor